The present invention relates to the field of active polyphase filter design. More particularly, the invention relates to the use of transconductors to cross-couple active polyphase filters sections.
Polyphase filters receive an N-phase (or polyphase) input signal and create an N-phase output signal. A quadrature filter is a four-phase polyphase filter. In a quadrature filter, the input will consist of four signal voltages of mutually equal value. These four input signals jointly constituting a signal vector group with the individual signal vectors succeeding one another in a given direction of rotation through phase angles of 90 degrees. Dependent on direction of rotation, counter-clockwise or clockwise, the frequency of the polyphase signal is positive or negative. The I degree and 180 degree signal vectors are designated the +1 and xe2x88x92I signals. The 90 degree and 270 degree signal vectors are designated the +jQ and xe2x88x92jQ signals. Such a polyphase filter is known from the article xe2x80x9cAsymmetric Polyphase Networksxe2x80x9d by M. J. Gingell, published in xe2x80x9cElectrical Communicationxe2x80x9d, Vol. 48, no. 1 and 2, 1973, pp. 21-25.
Passive LC filters are limited by the difficulty of incorporating inductors into integrated circuits. To replace inductors and reduce sensitivity to component variations, active-RC filters were introduced. Operational amplifiers and, in some designs, gyrators are the reactances in an active-RC design. Active-RC filter circuits are easier to design and manufacture than passive filters. Feedback loops between the inputs and outputs of the active-RC reactances replace the need for inductive elements and reduce sensitivity to component variation.
The conversion of passive-LC filters designs to active-RC filter designs, termed xe2x80x9cfilter design,xe2x80x9d is the subject of many publications. Filter design begins with the choice of a passive filter. The most common types of passive filters are the gaussian, Butterworth, Bessel, and Chebyshev filters. The type of passive filter is chosen based upon its characteristics, such as ripple, stopband rejection, pole quality factor, noise figure, and sensitivity. The order of the filter, an indication of the number of poles in the filter, is also chosen. The choice of filter type and order is based on the constraints of the intended manufacturing process and end-use. After a filter type and order are chosen, nodal transfer functions (generally represented in Laplace notation) for the filter are derived. e nodal transfer functions allow a signal flow graph of the passive filter to be mapped. The noaltransfer functions of the passive filter are then replaced with active elements, resistors, and capacitors. The resulting active-RC filter network has a filter transfer function equivalent to the passive filter.
Three books that demonstrate filter design techniques are: (i) Handbook of Filter Synthesis, by Anatol I. Zverev, published 1967 by John Wiley and Sons; (ii) Electronic Filter Design Handbook, by Arthur B. Williams, published 1995 by McGraw Hill; and (iii) Analog MOS Integrated Circuits for Signal Processing, by Roubik Gregorian and Gabor C. Temes, published 1986 by John Wiley and Sons. In these books, schematics and tables of figures detail XT the configuration and component values for a broad range of filter types and orders. A detailed example of filter design can also be found in the following U.S. Patents: (i) xe2x80x9cSymmetrical Polyphase Networks Utilizing Constant Reactancesxe2x80x9d by Michael John Gingell, number 3,618,133, issued 1971; and (ii) xe2x80x9cAsymmetric Polyphase Filterxe2x80x9d by Johannes O. Voorman, number 4,914,408, issued 1990 (hereafter xe2x80x9cVoorman Patentxe2x80x9d). Computer programs for filter design are also available.
An example of filter design is illustrated in FIGS. 1A and 1B. FIG. 1A shows a low-pass third-order passive LC filter 1 with four nodes, N1, N2, N3, and N4, numbered sequentially clockwise from the top left. The input voltage Vin is applied across N1 and N4. The output voltage Vout is measured across N3 and N4. A first resistor RP1 is connected between N1 and N2. A first capacitor CP1 is connected between N2 and N4. An inductor LP1 is connected between N2 and N3. A second capacitor CP2 and a second resistor RP2 are connected in parallel across N3 and N4.
FIG. 1B shows a low-pass third-order active-RC filter block (hereafter xe2x80x9cFBxe2x80x9d) that approximates the transfer function of the low-pass third-order passive LC filter shown in FIG. 1A. FB includes: two input terminals IA and IB; two output terminals OA and OB; three reactances X1, X2, and X3; and fourteen matched resistors R. Each reactance is an active balanced integrating circuit than includes: one balanced differential amplifier 2, a reactance input pair 3; a reactance output pair 4; and a matched capacitor pair C1, C2, and C3. In each matched capacitor pair: one capacitor is shunted between the first input of a reactance input pair 3 and the first output of the reactance output pair 4; and the other capacitor is shunted between the second input of the reactance input pair 3 and the second output of the reactance output pair 4.
The internal nodes of FB can be identified by their associated terminal 5, as set forth in below Table I below.
Note also that output terminal OA is attached to terminal T3C and that output OB is attached to terminal T3D. The Table II netlist below indicates the location of the fourteen matched resistors R. In table II, one matched resistor R is connected between the first node and the second node.
While resistors R are shunted across X1 and X3, no resistors R are shunted across X2.
FIG. 1C shows a block diagram of FB. The block diagram has two inputs IA and IB. The block diagram has two outputs OA and OB. The block diagram also has three sets of four-lead terminals T1-T3 for a total of twelve terminals. The first set is labeled T1 and is composed of four terminals T1A, T1B, T1C, and T1D. The second set is labeled T2 and is composed of four terminals T2A, T2B, T2C, and T2D. The third set is labeled T3 and is composed of four terminals T3A, T3B, T3C, and T3D. Figure IC also demonstrates how FB can be attached to a 2-phase input +Iin and xe2x88x92Iin, by input terminals IA and IB respectively, to generate a 2-phase output +Iout and xe2x88x92Iout, through output terminals OA and OB respectively.
A second example of filter design is shown in FIGS. 1D and 1E. FIG. 1D shows a low-pass sixth-order passive LC filter 6 with six nodes, NZ1, NZ2, NZ3, NZ4, NZ5, and NZ6, numbered sequentially clockwise from the top left. The input voltage Vzin is applied across NZ1 and NZ6. The output voltage Vzout is measured across NZ5 and NZ6. A first resistor RPZ1 is connected between NZ1 and NZ2. A first capacitor CPZ1 is connected between NZ2 and NZ6. A first inductor LPZ1 is connected between NZ2 and NZ3. A second capacitor CPZ2 is connected between NZ3 and NZ6. A second inductor LPZ2 is connected between NZ3 and NZ4. A third capacitor CPZ3 is connected between NZ4 and NZ6. A third inductor LPZ3 is connected between NZ4 and NZ5. A second resistor RPZ2 is connected between NZ5 and NZ6.
FIG. 1E shows a low-pass sixth-order active-RC filter block (hereafter xe2x80x9cFBZxe2x80x9d) that approximates the transfer function of the low-pass sixth-order passive LC filter shown in FIG. 1D. FBZ includes: two input terminals IZA and IZB; two output terminals OZA and OZB; six reactances XZ1, XZ2, XZ3, XZ4, XZ5, and XZ6; and twenty-six matched resistors RZ. Each reactance is an active balanced integrating circuit than includes: one balanced differential amplifier 2, a reactance input pair 3; a reactance output pair 4; and a matched capacitor pair CZ1, CZ2, CZ3, CZ4, CZ5, and CZ6. In each matched capacitor pair: one capacitor of each matched pair is shunted between the first input of a reactance input pair 3 and the first output of the reactance output pair 4; and the other capacitor is shunted between the second input of the reactance input pair 3 and the second output of the reactance output pair 4.
The internal nodes of FBZ can be identified by their associated terminal 5, as set forth in Table III below.
Note also that the output terminal OZA is attached to TZ6A and that the output terminal OZB is attached to TZ6B. The Table IV netlist below indicates the location of the twenty-six matched resistors RZ. In the table, one matched resistor RZ is connected between the first node and the second node.
While resistors RZ are shunted across XZ1 and XZ6, no resistors RZ are shunted across XZ2, XZ3, XZ4, or XZ5.
FIG. 1F shows a block diagram of FBZ. The block diagram has two inputs IZA and IZB. The block diagram has two output terminals OZA and OZB. The block diagram also has six sets of four-lead terminals for a total of twenty-four terminals. The first set is labeled TZ1 and is composed of four terminals TZ1A, TZ1B, TZ1C, and TZ1D. The second set is labeled TZ2 and is composed of four terminals TZ2A, TZ2B, TZ2C, and TZ2D. The third set is labeled TZ3 and is composed of four terminals TZ3A, TZ3B, TZ3C, and TZ3D.
The fourth set is labeled TZ4 and is composed of four terminals TZ4A, TZ4B, TZ4C, and TZ4D. The fifth set is labeled TZ5 and is composed of four terminals TZ5A, TZ5B, TZ5C, and TZ5D. The sixth set is labeled TZ6 and is composed of four terminals TZ6A, TZ6B, TZ6C, and TZ6D. FIG. 1F also demonstrates how FBZ receives a 2-phase input +Iin and xe2x88x92Iin, by input terminals IZA and IZB respectively, to generate a 2-phase output signal +Iout and xe2x88x92Iout, through output terminals OZA and OZB respectively.
FIGS. 2A and 2B demonstrate how low-pass quadrature filters can be constructed from a first filter section 7 for the I signals and a second filter section 8 for the Q signals. FIG. 2A shows a first filter section FB and a second filter section FBxe2x80x2. Both FB and FBxe2x80x2 are identical to the third-order low-pass active RC filter illustrated in FIGS. 1B and 1C. The first filter section FB is attached to a 2-phase input +Iin and xe2x88x92Iin, by FB input terminals IA and IB respectively, to generate a 2-phase output +Iout and xe2x88x92Iout, through FB output terminals OA and OB respectively. The second filter section FBxe2x80x2 is attached to a 2-phase input +Qin and xe2x88x92Qin, by FBxe2x80x2 input terminals IAxe2x80x2 and IBxe2x80x2 respectively, to generate a 2-phase output +Qout and xe2x88x92Qout, through FBxe2x80x2 output terminals OAxe2x80x2 and OAxe2x80x2 respectively. The terminals of FB and FBxe2x80x2 are not used in this configuration.
FIG. 2B shows a first filter section FBZ and a second filter section FBZxe2x80x2. The first filter section FBZ and the second filter section FBZxe2x80x2 are both identical to the low-pass sixth-order active RC filter illustrated in FIGS. 1E and 1F. The first filter section FBZ is connected to inputs +Iin and xe2x88x92Iin by input terminals IZA and IZB, respectively, and to outputs +Izout and xe2x88x92Izout by ouput terminals OZA and OZB, respectively. The second filter section FBZxe2x80x2 is connected to inputs +Qin and xe2x88x92Qin by input terminals IZAxe2x80x2 and IZBxe2x80x2, respectively, and to outputs +Qzout and xe2x88x92Qzout by output terminals OZAxe2x80x2 and OZBxe2x80x2, respectively. The terminals of FBZ and FBZxe2x80x2 are not used in this configuration.
Though the circuit path for the I and Q signal inputs never intersect each other in the circuits shown in FIGS. 2A and 2B, the two filter sections perform as a low-pass sixth-order quadrature filter and low-pass twelfth-order quadrature filter, respectively. Since the bandpass of the quadrature filter includes both low positive frequencies and low negative frequencies, the quadrature filters shown in FIGS. 2A and 2B act like band-pass filters with a center frequency of zero hertz.
The Voorman Patent (U.S. Pat. No. 4,914,408) discloses that a quadrature band-pass filter can be created by cross-coupling the reactances of two filter sections with matched resistors. Application of this approach can be accomplished by shunting matched resistors between the terminals 5 of the first filter section FBZ and the terminals 5 of the second filter section FBZxe2x80x2.
To simplify representation of the matched resistors, FIGS. 3A to 3D describe two resistor coupling blocks and their contents. FIG. 3A shows three sets of four matched resistors, R1, R2 and R3. Each resistor has a node on either end. The node netlist for each resistor is set forth in Table V below.
FIG. 3B shows the resistor coupling block diagram labeled xe2x80x9cR block.xe2x80x9d The R block has 24 leads. The leads are grouped into sets of four leads labeled RC1, RC2, RC3, RC1xe2x80x2, RC2xe2x80x2, and RC3xe2x80x2. Each set has an A, B, C, and D lead. RC1, for instance, has leads RC1A, RC1B, RC1C, and RC1D. And RC1xe2x80x2 has leads RC1Axe2x80x2, RC1Bxe2x80x2, RC1Cxe2x80x2, and RC1Dxe2x80x2.
FIGS. 3C and 3D describe the resistor block for FBZ. FIG. 3B shows six sets of four matched resistors, RZ1, RZ2, RZ3, RZ4, RZ5, and RZ6. Each resistor has a node on either end. The node netlist for each resistor is set forth in Table VI below.
FIG. 3D shows the resistor coupling block diagram labeled xe2x80x9cRZ block.xe2x80x9d The RZ block has forty-eight leads. The leads are grouped into sets of four leads labeled RZC1, RZC2, RZC3, RZC4, RZC5, RZC6, RZC1xe2x80x2, RZC2xe2x80x2, RZC3xe2x80x2, RZC4xe2x80x2, RZC5xe2x80x2, and RZC6xe2x80x2. Each set has an A, C, and D lead.
FIGS. 4A shows a first filter section FB and a second filter section FBxe2x80x2 coupled together through an R block. Excluding the addition and coupling of the R block, FIG. 4A shows the same quadrature filter configuration as in FIG. 2A. Corresponding R block leads are connected to the terminals of the first filter section FB and the section filter section FBxe2x80x2. RC1A and RC1Axe2x80x2, for instance, are connected to T1A and T1Axe2x80x2 respectively. The coupling of the first filter section FB to the second filter section FBxe2x80x2 in FIG. 4B follows the same method as FIG. 4A, except that the RZ block is used to couple FBZ and FBZxe2x80x2.
Coupling the filter sections of a low-pass quadrature filter changes the quadrature filter in two ways. First, the coupling reduces the quadrature filter""s sensitivity to component variations between the first filter section FBZ and the second filter section FBZxe2x80x2. As the I and Q signals share many components, component variations effects have approximately the same impact upon each signal""s transfer function. A second result of the cross-coupling is that the center frequency of the quadrature filter is moved from zero hertz to a new center frequency. As disclosed in the Voorman Patent, the center frequency of the coupled filter is equal to 1/RiCi, where Ri is the value of an individual cross-coupling resistor between two corresponding reactances and Ci is the capacitance of an single matched capacitor shunted between the input and output of the corresponding reactances. During design of integrated circuits containing these active quadrature band-pass filters, the center frequency can be adjusted by adjusting the value of Ri and Ci.
The resistor cross-coupling disclosed in the Voorman Patent has some limitations. First, the center frequency cannot be altered post-manufacture, as resistors and capacitors are passive elements with non-adjustable values. Second, component variations between the first filter section and the second filter section can degrade output signal quality. The resistors are shunted across operational amplifiers, which are susceptible to variation in common mode voltage or DC offset voltage. A mismatch between corresponding operational amplifiers can result in larger than expected or smaller than expected currents through a coupling resistor. Larger than expected and smaller than expected currents can also result from component variations between matched capacitor and resistors.
The invention is an improved implementation of an active-RC polyphase band-pass filter with transconductor cross-coupling between filter sections. The polyphase filter has first to fourth inputs, first to fourth outputs, two filter sections, and a block of transconductor pairs. The four input signals to the polyphase filter succeed one another in phase by 90 degrees. The two filter sections have reactances comprised of active balanced operational amplifiers with matched capacitors in their feedback loops. Each transconductor pair of the block is coupled between corresponding reactances of each filter. The transconductance value of each transconductor pair is set as the product of a desired radian center frequency and the capacitance of the corresponding matched capacitors. In the preferred embodiment, the transconductors are Gm cells and the transconductance value of at least one Gm cell is field adjustable. This means that the transconductance value can be adjusted after the filter has been constructed or placed in service. The filter sections of the preferred embodiment can be a pair of low-pass, third-order, active-RC gaussian filters or a pair of low-pass sixth-order active-RC gaussian filters.
The first filter section has X-reactances and M-terminals. The second filter section has Y-reactances and N-terminals. The filter sections are coupled by the block of transconductors with a total of M plus N terminals. The X-reactances are coupled to the first input, the third input, the first output, and the third output. The Y-reactances are coupled to the second input, the fourth input, the second output, and the fourth output of the output. The M-terminals are coupled to select ones of the X-reactances. The N-terminals are coupled to select ones of the Y-reactances. In the preferred embodiment: X and Y are equal and M and N are equal; one half of the M-terminals are coupled to reactance input terminal pairs of the first filter section and the other half are coupled to reactance output terminal pairs of the first filter section; and one half of the N-terminals are coupled to reactance input terminal pairs of the second filter section and the other half are coupled to reactance output terminal pairs of the second filter section.
The reactances of each filter section are comprised of active balanced integrating circuits. Each active balance integrating circuit has a balanced differential operational amplifier with matched capacitors in their feedback loop. The balanced differential operational amplifier has a reactance input terminal pair and a reactance output terminal pair. The first matched capacitor is shunted between the first input of the reactance input terminal pair and the first output of the reactance output terminal pair. The second matched capacitor is shunted between the second input terminal of the reactance input terminal pair and the second output of the reactance output terminal pair. The matched capacitors of the first to Xth reactance and the corresponding matched capacitors of the first to Yth reactance are of equal capacitance.
The block of transconductors is composed of Z-transconductor pairs composed of Gm cells. Each of the Z-transconductor pairs cross-couple a reactance of the first filter section through its M-terminals and the correspoding reactances of the second filter section through its N-terminals. Each Gm cell has one transconductor input terminal pair and one transconductor output terminal pair. The transconductance value of each Gm cell is set as the product of a desired radian center frequency and the capacitance of the nearest matched capacitors. In the preferred embodiment, the transconductance value of at least one Gm cell is field adjustable, permitting adjustment of the center frequency in the field.
In each Z-transconductor pair, one Gm cell is coupled by its transconductor input terminal pair to a reactance output terminal pair of a corresponding X-reactance through a selected pair of M-terminals and by its transconductor output terminal pair to a reactance input terminal pair of a corresponding Y-reactance through a selected pair of N-terminals. The second Gm cell in each Z-transconductor pair is coupled by its transconductor input terminal pair to a reactance output terminal pair of a corresponding Y-reactance through a selected pair of N-terminals and by its transconductor output terminal pair to a reactance input terminal pair of a corresponding X-reactance through a selected pair of M-terminals. As the inputs of each Gm cell are a differential voltage from a single reactance, variation in the common mode voltage or DC offset between the filter sections does not adversely affect the polyphase filter""s transfer function.